by Felipe F. Melo and Valéria C.F. Barbosa

This paper has been submitted for publication in the journal Computers & Geosciences.

This repository contains the source code to perform the first synthetic test presented. The codes euler_python.py, the synthetic data synthetic_data.dat of the first test presented in the paper and the codes synthetic_test.py, estimates_statistics.py and plot_functions.py to generate the results of the synthetic test related to our methodology.

The euler_python program is compatible with both Python 2.7 and Python 3.7 programming language.

We propose a novel methodology to select reliable Euler deconvolution estimates throughout the vertical derivatives of the total-field anomaly, grounded on the capability of this quantity to locate anomalies due to its higher signal decay with distance. In applying Euler deconvolution to a small moving-data window, we compute the standard deviation of the vertical derivatives of the total-field anomaly for each data window. Then, we define the reliable source-location estimates as those estimates that are obtained by using the data windows with the largest standard deviations of the vertical derivatives of the total-field anomaly. For all tentative values of the structural index (SI), the reliable estimates with tight clustering define the correct SI and the mean of these estimates define the source position. We compared our methodology to select reliable Euler source-position estimates with two available methodologies in the literature based on the rejection criteria of data amplitude and of depth uncertainty. We conducted tests on synthetic noise-corrupted data to investigate the sensitivity of our method to deal with the presence of: i) an additive nonlinear background that simulates a regional field; ii) interfering anomalies with distinct amplitudes; iii) weak-, mid-, and strong-interfering anomalies; and iv) distinct noise levels. Most of tests in the sensitivity analysis shows that our methodology to select reliable Euler source-position estimates yielded better interpretation of the simulated magnetic sources than the methodology based on the rejection criteria of data amplitude and of depth uncertainty. The only exception was the tests with high noise levels in which the reliable Euler estimates selected either by our method or by the rejection criteria yielded poor interpretations. Applications to a real aeromagnetic survey from southern Brazil interpreted an isolated plug intrusion over the Anitápolis anomaly and a swarm of shallow-seated dikes with northwest-southeast trend over the Paranaguá Terrane.

• euler_python.py: General Python module containing the functions to compute de derivatives and Euler deconvolution.

• synthetic_test.py: Python script to generate the synthetic results. The script loads the total-field anomaly of a synthetic model from the file "synthetic_data.dat" and computes the Euler deconvolution using the functions in "euler_python.py". The results are generated using the functions "plot_functions.py" for the plots and "estimates_statistics.py" to compute the statistics of the data.

• plot_functions.py: Python script to generate the figures 2d, 4 and 7 of the first synthetic test.

• estimates_statistics.py: Python script to compute the mean of the northing, easting and depth estimates.

Test data:

• synthetic_data.dat: Synthetic total-field anomaly data generated using the Python packaged "Fatiando a Terra": http://fatiando.org/. This data is an example used in the current publication and shown in figure 2d.

You can download a copy of all the files in this repository by cloning the git repository:

git clone https://github.com/ffigura/Euler-deconvolution-python.git

or download a zip archive.

The Python program for Euler deconvolution "euler_python.py" and the scripts "synthetic_test.py" and "estimates_statistics.py" require the Python package "numpy", and the script "plot_functions.py" requires the Python packages "numpy" and "matplotlib". The easier way to get Python and all libraries installed is through the Anaconda Python distribution (https://www.anaconda.com/distribution/). After installed Anaconda, install the libraries by running the following command in your terminal:

conda install numpy matplotlib

The program for Euler deconvolution "euler_python.py" and the additional codes "synthetic_test.py", "plot_functions.py" and "estimates_statistics.py" are compatible with both Python 2.7 and 3.7.

The results and figures (2d, 4 and 7) for the synthetic test are reproducible from the folder /test_4_sources. Running the code synthetic_test.py will allow the reprodution of the results of our methodology. For more information read the file README.MD or README.txt in the folder /code.

All source code is made available under a BSD 3-clause license. You can freely use and modify the code, without warranty, so long as you provide attribution to the authors. See LICENSE.md for the full license text.

The manuscript text is not open source. The authors reserve the rights to the article content, which is currently submitted for publication in the Computers & Geosciences.